Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;

class Pair<E extends Comparable<E>,F extends Comparable<F>> implements Comparable<Pair<E,F>>{
    E first;
    F second;
    public Pair(E first, F second){
        this.first=first;
        this.second=second;
    }
    public E getFirst(){return first;}
    public F getSecond(){return second;}
    public String toString(){
        return "<"+first.toString()+","+second.toString()+">";
    }
    public int hashCode(){
        return first.hashCode()*30011+second.hashCode()+2;
    }
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair another = (Pair) obj;
        return this.getFirst().equals(another.getFirst())&&this.getSecond().equals(another.getSecond());
    }

    public int compareTo(Pair<E,F> another){
        if(this.getFirst().equals(another.getFirst())){
            return this.getSecond().compareTo(another.getSecond());
        }
        return this.getFirst().compareTo(another.getFirst());
    }

}
class ArrayLib{
    static<E extends Comparable<E>> E getOrDefault(E[] array, int index, E defaultValue){
        if(index<0 || index>=array.length) return defaultValue;
        return array[index];
    }

    static<E extends Comparable<E>> int maxIndexOfArray(E[] a){
        int ans = 0;
        for(int i=1;i<a.length;i++){
            if(a[i].compareTo(a[ans])>0) ans=i;
        }
        return ans;
    }
    static<E extends Comparable<E>> int minIndexOfArray(E[] a){
        int ans = 0;
        for(int i=1;i<a.length;i++){
            if(a[i].compareTo(a[ans])<0) ans=i;
        }
        return ans;
    }

    // minimum x st. array[x] >= elm
    static<E extends Comparable<E>> int lowerBound(E[] array, E elm){
        if(array[0].compareTo(elm)>=0) return 0;
        int min = 0, max = array.length;
        // array[min] < elm
        // array[max] >= elm
        while(min+1<max){
            int mid = (min+max)/2;
            if(array[mid].compareTo(elm) < 0) min = mid;
            else max = mid;
        }
        return max;
    }
    // minimum x st. array[x] > elm
    static<E extends Comparable<E>> int upperBound(E[] array, E elm){
        if(array[0].compareTo(elm)>0) return 0;
        int min = 0, max = array.length;
        // array[min] <= elm
        // array[max] > elm
        while(min+1<max){
            int mid = (min+max)/2;
            if(array[mid].compareTo(elm) <= 0) min = mid;
            else max = mid;
        }
        return max;
    }
    static<E extends Comparable<E>> int count(E[] array, E elm){
        return upperBound(array,elm)-lowerBound(array,elm);
    }

    static boolean nextPermutation(List<Integer> list){
        int pivotPos = -1;
        int pivot = 0;
        for (int i=list.size()-2; i>=0; i--) {
            if (list.get(i) < list.get(i+1)) {
                pivotPos = i;
                pivot = list.get(i);
                break;
            }
        }

        if (pivotPos==-1 && pivot==0) return false;

        int L = pivotPos+1, R = list.size()-1;
        int minPos = -1;
        int min = Integer.MAX_VALUE;
        for (int i=R; i>=L; i--) {
            if (pivot < list.get(i)) {
                if (list.get(i) < min) {
                    min = list.get(i);
                    minPos = i;
                }
            }
        }

        Collections.swap(list, pivotPos, minPos);
        Collections.sort(list.subList(L, R+1));

        StringBuilder sb = new StringBuilder();
        for (int i=0; i<list.size(); i++) sb.append(list.get(i));

        return true;
    }
}

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int A = sc.nextInt();
        int B = sc.nextInt();
        Long[] V = new Long[N];
        for(int n=0; n<N; n++) V[n]=sc.nextLong();
        Arrays.sort(V);

        double sum = 0;
        for(int a=0; a<A; a++) sum += V[N-1-a];
        System.out.printf("%.10f\n",sum/A);

        long lastItemValue = V[N-A];

        int lastItemMin, lastItemMax;

        lastItemMin = A - (N-ArrayLib.upperBound(V, lastItemValue));
        if(V[N-1]==lastItemValue) lastItemMax = Math.min(B, ArrayLib.count(V, lastItemValue));
        else lastItemMax = lastItemMin;


        long[][] combination = new long[100][100];
        combination[1][0]=1; combination[1][1]=1;
        for(int n=2; n<100; n++) for(int r=0; r<=n; r++) combination[n][r]=combination[n-1][r]+(r<=0?0:combination[n-1][r-1]);


        long ans = 0;

        for(int lastItem = lastItemMin; lastItem<=lastItemMax; lastItem++){
            ans += combination[ArrayLib.count(V,lastItemValue)][lastItem];
        }
        System.out.println(ans);
    }
}